Experience, causation, and induction › Two kinds of question

Section IV distinguishes relations of ideas from matters of fact. Hume places arithmetic, algebra, and geometry in the first group. His arithmetic example concerns the equality between three times five and half of thirty. Discovering such a relation does not depend on finding fifteen objects in the world. A statement about an actual event has a different status: its contrary can be intelligible even when we have overwhelming evidence against it. E 4.1–2.

Consider a simple comparison. Denying the equality of fifteen and half of thirty conflicts with the arithmetic relation. Denying that tomorrow's train will arrive punctually does not contradict the concept of a train. You can describe a delay without contradicting yourself. That possibility does not make a delay likely. It shows why a proof of an arithmetic relation and evidence for a future arrival are different achievements.

Hume asks how we reason about facts beyond what we presently perceive or remember. His answer is that such inferences depend on cause and effect. A letter can support a belief about an absent friend; an artifact can support an inference about its maker. In each case, a present fact functions as evidence for another because we take them to be connected. His question therefore concerns inference to absent and unobserved facts as well as prediction of the future. E 4.3–6.

Knowing a particular causal relation requires experience, Hume argues. The visible qualities of an entirely unfamiliar object do not reveal everything it can do. Without relevant experience, seeing water would not disclose that a person could drown in it. Once a connection becomes familiar, its effects can seem obvious from the cause itself. Hume wants us to notice how learning has disappeared from that feeling of obviousness. His argument concerns what unaided inspection and reasoning can establish, rather than whether later investigation can discover useful mechanisms. E 4.6–8.